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diff --git a/matita/matita/contribs/lambdadelta/ground/lib/ltc_ctc.ma b/matita/matita/contribs/lambdadelta/ground/lib/ltc_ctc.ma
index 54b1117b6..f598434a1 100644
--- a/matita/matita/contribs/lambdadelta/ground/lib/ltc_ctc.ma
+++ b/matita/matita/contribs/lambdadelta/ground/lib/ltc_ctc.ma
@@ -15,24 +15,24 @@
 include "ground/lib/star.ma".
 include "ground/lib/ltc.ma".
 
-(* LABELLED TRANSITIVE CLOSURE **********************************************)
+(* LABELLED TRANSITIVE CLOSURE FOR RELATIONS ********************************)
 
-alias symbol "subseteq" = "relation inclusion". (**)
+alias symbol "subseteq" = "relation inclusion". (* * alias *)
 
-(* Constructions with contextual transitive closure *************************)
+(* Constructions with ctc ***************************************************)
 
 lemma ltc_CTC (C) (A) (i) (f) (B) (R:relation4 C A B B):
-              left_identity … f i →
-              ∀c. CTC … (λc. R c i) c ⊆ ltc … f … (R c) i.
+      left_identity … f i →
+      ∀c. CTC … (λc. R c i) c ⊆ ltc … f … (R c) i.
 #C #A #i #f #B #R #Hf #c #b1 #b2 #H elim H -b2 /2 width=1 by ltc_rc/
 #b #b2 #_ #Hb2 #IH >(Hf i) -Hf /2 width=3 by ltc_dx/
 qed.
 
-(* Inversions with contextual transitive closure ****************************)
+(* Inversions with ctc ******************************************************)
 
 lemma ltc_inv_CTC (C) (A) (i) (f) (B) (R:relation4 C A B B):
-                  associative … f → annulment_2 … f i →
-                  ∀c. ltc … f … (R c) i ⊆ CTC … (λc. R c i) c.
+      associative … f → annulment_2 … f i →
+      ∀c. ltc … f … (R c) i ⊆ CTC … (λc. R c i) c.
 #C #A #i #f #B #R #H1f #H2f #c #b1 #b2
 @(insert_eq_1 … i) #a #H
 @(ltc_ind_dx A f B … H) -a -b2 /2 width=1 by inj/ -H1f